Test Functions Space in Noncommutative Quantum Field Theory

Abstract

It is proven that the $\star$-product of field operators implies that the space of test functions in the Wightman approach to noncommutative quantum field theory is one of the Gel'fand-Shilov spaces $S^{\beta }$ with $\beta <1/2$. This class of test functions smears the noncommutative Wightman functions, which are in this case generalized distributions, sometimes called hyperfunctions. The existence and determination of the class of the test function spaces in NC QFT is important for any rigorous treatment in the Wightman approach.

10 pages, clarification of formula (1.6), typos fixed, minor language corrections

Cited by in corpus (10)

• Moyal multiplier algebras of the test function spaces of type S
• Duality covariant quantum field theory on noncommutative Minkowski space
• Algebras with convergent star products and their representations in Hilbert spaces
• Twisted convolution and Moyal star product of generalized functions
• Divergences in quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential
• UV/IR duality in noncommutative quantum field theory
• Noncommutative deformations of quantum field theories, locality, and causality
• Noncommutative Time in Quantum Field Theory
• Haag's Theorem in Noncommutative Quantum Field Theory
• Irreducibility of the set of field operators in Noncommutative Quantum Field Theory